Sentence examples for and the second variation from inspiring English sources

In particular it is shown that the first variation vanishes and the second variation is nonpositively definite.

SC shows a prominent bipolar change at auroral latitudes, in which the first variation is called the preliminary impulse (PI) and the second variation is called the main impulse (MI) (Araki 1994).

The problem is considered in two variations; in the first variation no restriction is imposed on the symmetricity of lane allocations for two-way streets, and in the second variation, two-way street lane allocations are restricted to be symmetric.

We derive a combinatorial formula for the second variation and prove that it is positive definite except along the first eigenspace, where it vanishes.

The map u is stationary for Φ if it is a critical point of (Phi (u)) with respect to any compact supported variation of u, and u is stable if the second variation for the functional (Phi (u)) is nonnegative.

She can show both humor and fervor but, as "Danses Concertantes" and the first variation in "Divertimento No. 15" showed, she lacks technical strength and doesn't project powerfully enough.

The solo piano work begins with an alluring modal theme, supported by tremolando chords, and in the first variation those elements are dissected, redistributed across the keyboard's range.

roughly speaking, we should have begin{aligned} frac{delta F}{delta varrho } varrho ^tau _{k+1})+frac{varphi }{tau }=const end{aligned} (4.11)(where the reasons for having a constant instead of 0 is the fact that, in the space of probability measures, only zero-mean densities are considered as admissible perturbations, and the first variations are always defined up to additive constants).

Dena Abergel had clarity and energy in the first variation.

Kathryn Morgan, the third new soloist, has a wonderfully oddball dramatic look, more operatic than dance, and she performed the fourth variation with such amiable confidence that she suggested an indulgent young mother putting her baby — the choreography — sweetly to bed.

Add fingers 2, 3, and 4 as you did with the first variation, and strum all the strings.